#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 18; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } LDP operator*(const LDP& a, const LDP& b) { return LDP{ a.first * b.first - a.second * b.second , a.first * b.second + a.second * b.first }; } LDP operator+(const LDP& a, const LDP& b) { return LDP{ a.first + b.first,a.second + b.second }; } LDP operator-(const LDP& a, const LDP& b) { return LDP{ a.first - b.first,a.second - b.second }; } //非再帰 //eps=0.01を忘れずに typedef vector poly; poly dft(poly f, bool inverse = false) { int n = f.size(); int i, j, k; //bit左右反転 for (i = 0, j = 1; j < n - 1; j++) { for (k = n >> 1; k > (i ^= k); k >>= 1); if (i > j)swap(f[i], f[j]); } for (int m = 2; m <= n; m *= 2) { LDP zeta = { cos(2 * pi / (ld)m), sin(2 * pi / (ld)m) }; if (inverse) { zeta = { cos(2 * pi * (m - 1) / (ld)m), sin(2 * pi * (m - 1) / (ld)m) }; } for (i = 0; i < n; i += m) { LDP powzeta = { 1,0 }; for (k = i; k < i + m / 2; k++) { LDP t1 = f[k], t2 = powzeta * f[k + m / 2]; f[k] = t1 + t2; f[k + m / 2] = t1 - t2; powzeta = powzeta * zeta; } } } if (inverse) { for (i = 0; i < n; i++) { f[i].first /= (ld)n; f[i].second /= (ld)n; } } return f; } poly multiply(poly g, poly h) { int n = 1; int sz = g.size() + h.size(); while (n <= sz)n *= 2; while (g.size() < n) { g.push_back({ 0,0 }); } while (h.size() < n) { h.push_back({ 0,0 }); } poly gg = dft(g); poly hh = dft(h); poly ff; rep(i, n) { ff.push_back(gg[i] * hh[i]); } return dft(ff, true); } struct bigint { string s; bigint() {}; bigint(ll n) { s = to_string(n); }; bigint(string t) { s = t; }; }; bool operator==(const bigint& a, const bigint& b) { return a.s == b.s; }; bool operator==(const bigint& a, const int& b) { return a.s == to_string(b); }; bool operator!=(const bigint& a, const bigint& b) { return !(a == b); }; bool operator!=(const bigint& a, const int& b) { return a != to_string(b); }; bool operator<(const bigint& a, const bigint& b) { if (a.s.length() != b.s.length())return a.s.length() < b.s.length(); return a.s < b.s; } bool operator>(const bigint& a, const bigint& b) { if (a.s.length() != b.s.length())return a.s.length() > b.s.length(); return a.s > b.s; } bool operator>=(const bigint& a, const bigint& b) { return !(a < b); } bool operator<=(const bigint& a, const bigint& b) { return !(a > b); } bigint operator+(const bigint& a, const bigint& b) { int len = max(a.s.length(), b.s.length()); bigint ret; bool f = false; rep(i, len) { int c = 0; if (f)c = 1, f = false; int j = a.s.length() - 1 - i; if (j >= 0)c += a.s[j] - '0'; j = b.s.length() - 1 - i; if (j >= 0)c += b.s[j] - '0'; if (c >= 10)f = true, c -= 10; ret.s.push_back('0' + c); } if (f)ret.s.push_back('1'); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator+(const bigint& a, const int b) { return a + bigint(b); } bigint operator-(const bigint& a, const bigint& b) { int len = max(a.s.length(), b.s.length()); bigint ret; bool f = false; rep(i, len) { int c = 0; if (f)c = -1, f = false; int j = a.s.length() - 1 - i; if (j >= 0)c += a.s[j] - '0'; j = b.s.length() - 1 - i; if (j >= 0)c -= b.s[j] - '0'; if (c < 0)f = true, c += 10; ret.s.push_back('0' + c); } while (ret.s.size() > 1 && ret.s.back() == '0')ret.s.pop_back(); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator/(const bigint& a, const bigint& b) { bigint ret(0); bigint ans; int len = a.s.length(); rep(i, len) { ret = ret + (a.s[i] - '0'); int cnt = 0; while (ret >= b)++cnt, ret = ret - b; ans.s.push_back('0' + cnt); if (ret != 0)ret.s.push_back('0'); } rep(i, ans.s.length()) { if (ans.s[i] != '0') { ans.s.erase(ans.s.begin(), ans.s.begin() + i); break; } if (i == (int)ans.s.length() - 1) { ans = 0; } } return ans; } bigint operator%(const bigint& a, const bigint& b) { bigint ret(0); int len = a.s.length(); rep(i, len) { ret = ret + (a.s[i] - '0'); while (ret >= b)ret = ret - b; if (ret != 0 && i < len - 1)ret.s.push_back('0'); } rep(i, ret.s.size()) { if (ret.s[i] != '0' || i == ret.s.size() - 1) { ret.s.erase(ret.s.begin(), ret.s.begin() + i); break; } } return ret; } bigint multi(const bigint& a, const int& t) { bigint ret; int c = 0; per(i, a.s.length()) { c += (a.s[i] - '0') * t; ret.s.push_back('0' + (c % 10)); c /= 10; } while (c > 0) { ret.s.push_back('0' + (c % 10)); c /= 10; } while (ret != 0 && ret.s.back() == '0')ret.s.pop_back(); reverse(ret.s.begin(), ret.s.end()); return ret; } bigint operator*(const bigint& a, const bigint& b) { poly p(a.s.size()); poly q(b.s.size()); rep(i, a.s.size()) { p[i] = { a.s[a.s.size() - 1 - i]-'0',0 }; } rep(i, b.s.size()) { q[i] = { b.s[b.s.size() - 1 - i] - '0',0 }; } poly r = multiply(p, q); bigint res; int c = 0; int loc = 0; while (true) { if (loc >= r.size() && c == 0)break; if (loc < r.size())c += (r[loc].first + 0.01); loc++; res.s.push_back('0' + c % 10); c /= 10; } while (res.s.size() > 1 && res.s.back() == '0')res.s.pop_back(); reverse(all(res.s)); return res; } bigint min(const bigint& a, const bigint& b) { if (a < b)return a; else return b; } bigint gcd(bigint a, bigint b) { if (a < b)swap(a, b); while (b > 0) { bigint r = a % b; a = b; b = r; } return a; } typedef pair bP; typedef vector> mat; typedef vector vec; mat mtmul(mat& A, mat& B) { mat C(A.size(), vec(B[0].size())); rep(i, (int)A.size()) { rep(k, (int)B.size()) { rep(j, (int)B[0].size()) { C[i][j] = (C[i][j] + (A[i][k] * B[k][j])); } } } return C; } mat mtpow(mat A, ll n) { mat B(A.size(), vec(A.size())); rep(i, (int)A.size()) { B[i][i] = 1; } while (n > 0) { if (n & (ll)1)B = mtmul(B, A); A = mtmul(A, A); n >>= 1; } return B; } bigint dp[2]; bigint calc(ll n) { mat A = { {1,1},{1,0} }; A = mtpow(A, n); return A[0][1]; } void solve() { ll n; cin >> n; if (n == 2) { cout << "INF\n"; cout << 0 << "\n"; return; } bigint ans = calc(n); bigint p = calc(n / 2); if (n % 2 == 0)ans = ans - calc(n / 2) * calc(n / 2); cout << n << "\n"; cout << ans.s << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(15); //init_f(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }